I love tamarind which I first encountered while living in an East Indian community in Toronto. I've tried various pastes and concentrated forms of it, but eventually I realised I preferred the taste of "wet tamarind" the best. It involves a bit of work, but I process the entire package at once and freeze the remainder in ice cube trays for later use.
Wet tamarind is sold in small blocks and I look for packages which feel soft, avoiding the hard ones.
1 14oz package wet tamarind
about 2 1/2 - 3 cups very hot water
Using the back of a large spoon (or even your fingers) work to break up the tamarind pulp as best you can.
Force small amounts through a sieve. Set aside the bits that didn't go through.
Pour another cup of hot water over the reserved pulp (from the sieve) and leave for about 5 minutes. Stir it a few times and then force small amounts though the sieve again until there's no more remaining.
Occasionally I will do this a third time, adding about 1/2 cup of water. It all depends on how much paste I was able to express the first two times.
This will provide you with about 2 1/2 to 3 cups of delicious tart tamarind paste. It will keep refrigerated for a couple of weeks if you decide not to freeze it.